Informatica

Nowadays, environmental awareness and green marketing have become an important issue. Hybrid vehicles have created a significant improvement in environmental issues. The main aims of efforts in purchasing hybrid vehicles are decreasing greenhouse effect and protecting the environment by reducing carbon dioxide emission (Soon et al., 2013; Zhao et al., 2021). For the smart consumers, the purchasing process of hybrid vehicles is not easy because of the many alternatives with different brands including different selection criteria. So, the hybrid vehicle selection problem is regarded as an MCDM problem in this paper. The main criteria or factors affecting hybrid vehicle selection are hybrid type, the powertrain features, the vehicle’s price, safety and reliability.

In the literature, there are several studies about revealing the criteria or factors on this selection. Ucarol et al. (2005) compared non-hybrid vehicle with series and parallel hybrid vehicles in terms of energy consumption and performance. Safaei Mohamadabadi et al. (2009) ranked the renewable and non-renewable transportation fuel vehicles. Tzeng et al. (2005) and Vahdani et al. (2011) investigated social, economic, technological, and transportation aspects of evaluation criteria for alternative-fuel buses selection. Soon et al. (2013) determined hybrid/electric vehicle selection criteria as financial condition, consumer awareness, quality of vehicle and demographic background of consumers. Hong et al. (2013) investigated the association between demographic factors and selection of hybrid vehicles among Malaysians. Yavuz et al. (2015) evaluated the alternative-fuel vehicles considering purchase and operation costs, safety, perceived quality, performance, filling station availability, filling time, driving range, greenhouse gas emission, social welfare impact, market penetration, secondary market development criteria with hesitant fuzzy linguistic term sets (HFLTS). Neizari et al. (2017) considered four main factors such as price sensitivity, environmental awareness, green perceived value, and green trust. Biswas and Das (2018) considered five criteria, and used MABAC method for the selection of hybrid car. Arat (2018) selected electric motors and compared the different driving cycles’ effects. İç and Şimşek (2019) developed a model including Taguchi-TOPSIS methods for the hybrid electrical automobile selection problem. Khan et al. (2020) selected the most sustainable hybrid electric vehicle in Pakistan based on economic, environmental, and social criteria. Sonar and Kulkarni (2021) combined AHP and MABAC methods for electric vehicle selection considering six criteria. Tran et al. (2021) examined many powertrain configurations and components for the hybrid powertrain design purpose that can satisfy the performance criteria as acceleration, braking, driving range, fuel economy, and emissions. Hezam et al. (2022) assessed alternative fuel vehicles (hybrid electric vehicles, electric vehicles, hydrogen vehicles, natural gas vehicles, and biofuel vehicles) with an integrated decision-making framework based on intuitionistic fuzzy MEREC, RS and DNMA for sustainable road transportation. They considered environmental, technical, economic, social, and political dimensions of criteria. According to the results, the most significant criteria are social benefits, fueling/charging infrastructure, and financial incentives, respectively. Bošković et al. (2023) solved the electric vehicle selection problem for the last-mile delivery according to price, payload, width, battery capacity, and volume with the AROMAN method. Sharma and Maitra (2024) tried to reveal key attributes that affect the plug-in hybrid electric vehicle adaptation with exploratory factor and grey relation analyses. Golui et al. (2024) ranked the eight electric vehicle alternatives with Fermatean fuzzy TOPSIS. Table 1 shows the summary of MCDM studies on criteria affecting hybrid vehicle selection.

There are several researchers who have integrated the AHP method with IF sets. Sadiq and Tesfamariam (2009) introduced IF AHP method and solved case studies for the applicability of the method. Abdullah et al. (2009) developed a new AHP method and used only membership and non-membership functions as IF set preference measurement notation. Hai et al. (2011) focused on eigenvectors synthesis of the IF comparison matrix in IVIF AHP method. Xu and Liao (2013) and Wu et al. (2013) developed IF AHP method for handling comprehensive MCDM problems. Abdullah and Najib (2014) used the IF AHP method including a new preference scale for pairwise comparisons. Fahmi et al. (2015) selected the assistant for a university with IVIF AHP method. Abdullah and Najib (2016) developed a new preference scale for pairwise comparison measurement for IVIF AHP method and demonstrated a case study related to sustainable energy planning selection. Deepika and Karthik Kannan (2016) selected a global supplier with IF AHP method. Kahraman et al. (2016) evaluated outsourced manufacturers with IVIF AHP and TOPSIS methods. Büyüközkan et al. (2016) evaluated hospital web services with IF AHP and IF VIKOR methods. Tooranloo and Iranpour (2017) selected an appropriate supplier by performing IVIF AHP method. Büyüközkan et al. (2018) combined IVIF AHP method with IVIF extensions of COPRAS, MULTIMOORA, TOPSIS and VIKOR methods for cloud computing technology selection. Seker (2020) selected the best solar power plant site by performing IVIF AHP and IVIF COPRAS methods. Büyüközkan et al. (2021a) evaluated the digital competency of low-cost airlines with IVIF AHP and IVIF VIKOR methods. Ilbahar et al. (2021a) integrated IVPF BOCR and IVIF AHP methods for social acceptability assessment of renewable energy policies. Ilbahar et al. (2021b) used IVIF AHP and fuzzy axiomatic design for risk assessment of R&D projects. Tumsekcali et al. (2021) used IVIF AHP-WASPAS methods for public transportation service quality evaluation. Ayyildiz (2021) used IVIF AHP for green supply chain resilience evaluation. Lu et al. (2022) used IVIF AHP and FCE methods to assess the overall status of urban mobility. Wang et al. (2023b) proposed a method for evaluating the feasibility of a distribution network operation scheme based on an IVIF AHP. Acar et al. (2024) performed IVIF AHP for evaluating the sustainability performance of the selected stationary hydrogen storage options. Mandal et al. (2024) proposed a methodology based on IVIF AHP and IVIF TOPSIS for PhD supervisor selection. Bouraima et al. (2024) presented a solution methodology based on SWOT, IVIF AHP, and IVIF TOPSIS for prioritizing the alternatives for the development of PV solar power. The studies based on AHP method with IF sets are summarized in Table 2.

The fuzzy and IF extensions of MABAC method have also been developed to resolve the uncertainty in problems. Xue et al. (2016) solved material selection problems with IVIF MABAC method. Peng and Yang (2016) showed the combination of MABAC method and Pythagorean fuzzy Choquet integral. Roy et al. (2016) combined MABAC method with type-2 fuzzy sets, and showed a case study related with personnel selection of a software company. Roy et al. (2017) presented the combination of AHP and MABAC methods with rough numbers, and applied the proposed methodology to a problem including tourism destinations evaluations. Yu et al. (2017) proposed an interval type-2 fuzzy MABAC method for selecting hotels from a tourism website. Pamučar et al. (2018) proposed to use interval valued fuzzy rough numbers in the integration of Best-Worst and MABAC methods. Sun et al. (2018) proposed hesitant fuzzy MABAC method for patients’ prioritization. Liu et al. (2019) used IVIF MABAC method for a novel integrated risk prioritization approach. Mishra et al. (2020) also used IVIF MABAC method for a programming language selection problem. Wang et al. (2020) introduced q-rung orthopair fuzzy MABAC method. Büyüközkan et al. (2021b) proposed hesitant fuzzy linguistic AHP and MABAC methods for the most appealing health tourism strategy selection. Puška et al. (2021) applied interval fuzzy logic using PIPRECIA and MABAC methods for sustainable supplier selection. Liu and Zhang (2021) proposed to integrate MABAC, CCSD, and prospect theory with normal wiggly hesitant fuzzy sets. Keshavarz-Ghorabaee et al. (2021) performed the combination of fuzzy BWM and MABAC for sustainable public transportation evaluation. Zhao et al. (2021) introduced the integration of IF MABAC method and cumulative prospect theory. Hashemkhani Zolfani et al. (2021) showed the combination of improved fuzzy SWARA and fuzzy MABAC methods for logistics village selection. Verma (2021) developed a fuzzy MABAC method by utilizing the developed fuzzy information measures. Liu and Wang (2021) improved the MABAC method with 2-dimensional uncertain linguistic variables for multi attribute group decision-making problems. Aydın (2021) extended MABAC method to Fermatean fuzzy sets whereas Mathew et al. (2021) extended MABAC method to interval valued Fermatean fuzzy sets. Zhang et al. (2021) used spherical fuzzy CPT-MABAC method while Wang et al. (2023c) used IVIF-CPT-MABAC method for green supplier selection. Kirişci (2024) performed a methodology combining interval valued Fermatean fuzzy AHP, TOPSIS, and MABAC for risk evaluation of self-driving vehicles. Huo et al. (2024) proposed an approach based on IVIF entropy, MABAC and TODIM methods for college English teaching quality evaluation. Jana et al. (2024) proposed logarithm bipolar fuzzy MABAC, and presented a case study to show the applicability of the method. Sundar Singh Sivam et al. (2024) proposed to apply IF MABAC for material selection. Chowdhury et al. (2024) used IF CRADID, EDAS, and MABAC for optimizing a surface grinding process. The studies based on the MABAC method with IF sets are summarized in Table 3.

As a result of the literature review, it is seen that the problem aimed to be solved in this study and the methods used are compatible with the literature. Namely, it is seen that there are studies on hybrid vehicle selection with different MCDM methods or extensions of MCDM methods with uncertainty theories. However, to the best of our knowledge, the hybrid vehicle selection problem, which is quite on the agenda today together with environmental awareness, has not been addressed in the IVIF environment yet. On the other hand, when evaluated on a method basis, it is seen that the IVIF extension of AHP, one of the subjective weighting methods, is used in many different MCDM problems such as supplier, plant, PhD student selection. A similar evaluation can be made for the IVIF MABAC method. However, our detailed literature review indicates that these methods are not used alone or in an integrated manner in the hybrid vehicle selection problem. In this sense, this study has the feature of filling this gap in the literature. On the other hand, the number of studies on the hybrid vehicle selection problem is quite few. This situation can be considered as a sign that both consumers and manufacturers cannot obtain sufficient information from the relevant literature on evaluating, analysing and selecting hybrid vehicles. In addition, since this problem has many conflicting criteria and the selection behaviour varies from person to person, therefore, considering the uncertainty inherent in the problem, it is important to express the criteria, weights and performances of the hybrid vehicles under the criteria with linguistic variables and to solve it with an effective uncertainty theory. Considering all these situations, a new decision-making methodology consisting of IVIF AHP and IVIF MABAC, which is presented for the first time in the literature, is proposed to address hybrid vehicle selection problems in an IVIF environment. In short, it is thought that the use of IVIFs to better express uncertainty in both methods will increase the flexibility of decision makers, effectively convey the opinions of decision makers to the decision-making process and ensure sound decisions are made.

Interval Valued Intuitionistic Fuzzy (IVIF) sets were developed firstly by Atanassov and Gargov (1989). IVIF sets can be defined as the generalization of both IVF sets and IF sets (Onar et al., 2015). An element’s membership and non-membership degrees belonging to an IVIF set are represented by the interval values in [0, 1].

The decision makers play an important role in the decision-making process. A decision maker makes qualitative and quantitative assessments of alternatives with conflicting criteria then ranks and/or selects the alternatives of the MCDM problem (Gupta et al., 2019). The problem involves single or multiple decision makers. The amount of complexity in the decision-making process increases as the number of decision makers increases. This type of problem, involving multiple decision makers, is called group decision making problems. The aim of group decision making is to aggregate the individual judgments into a group decision which is a true representative of the individual judgments (Gupta et al., 2018).

Decision makers may have different opinions owing to coming from different areas and having different expertise and experience. This affects the instability and inconsistency of the criteria weights and performance of the alternatives under each criterion. In other words, it will lead to unreliable results (Zhu, 2013; Liu et al., 2019). To get more rational results, a coefficient or a weight (importance degree) reflecting the decision maker’s ability may be assigned. If the difference between decision makers’ knowledge is clear, a direct valuation method may be applied. In this situation, the decision maker’s weight is an exact number. But if it is not clear, the weight may be defined with fuzzy numbers. In this paper, the decision maker’s weight will be expressed in linguistic terms and then, these terms are converted to IVIFNs. Firstly, it is assumed that there are K decision makers (DM_k, $k=1,2,\dots ,K$) in the problem. DM_k $([{\mu _{k}^{L}}(x),{\mu _{k}^{U}}(x)],[{v_{k}^{L}}(x),{v_{k}^{U}}(x)])$ is IVIFN for a rating of the kth decision maker, and kth decision maker’s weight is denoted by ${\lambda _{k}}$. Table 4 presents the linguistic terms for rating each decision maker. kth decision maker’s weight (${\lambda _{k}}$) is calculated by the following formula (Abdullah and Najib, 2016): where ${\lambda _{k}}\geqslant 0$ and ${\textstyle\sum _{k=1}^{K}}{\lambda _{k}}=1$. In this formula, ${\tilde{\lambda }_{k}}$ shows kth decision maker’s entropy weight, and this value is computed by following entropy formula proposed by Wei et al. (2011), Abdullah et al. (2019):

AHP is one of the well-known MCDM methods. It was firstly proposed by Saaty (1980) and since then it has been used extensively for several applications (Kundakcı et al., 2015). It depends on the pairwise comparison scale. Hierarchical structure is vital for this method. A hierarchy is formed with at least three levels including the goal, criteria, and alternatives (Abdullah et al., 2013).

The steps of IVIF AHP method are presented as follows (Abdullah and Najib, 2016; Büyüközkan and Göçer, 2017; Büyüközkan et al., 2018):

Step 1: The problem’s hierarchy is structured. The hierarchy consists of three levels including the goal, criteria, and alternatives, respectively.

Step 2: Firstly, the criteria are compared with respect to the goal by each DM. In other words, the pair-wise comparison matrix is constructed by each DM. The opinion in the pair-wise comparison matrix is expressed as linguistic terms, and each linguistic term is represented by an IVIFN. The linguistic terms given in Table 5 are used for expressing opinions.

Step 3: The pairwise comparison matrices are aggregated. Aggregation is performed in two steps.

Firstly, each decision maker’s pairwise comparison matrices on criteria are aggregated. The result is an aggregated IVIFN judgment matrix, ${\tilde{R}_{I}^{k}}={({\tilde{r}_{ij}^{k}})_{nxn}}$. Secondly, a group IVIF judgment matrix ${\tilde{R}_{G}}={({\tilde{r}_{ij}})_{nxn}}$ is formed. In this step, IVIFWA operator in Eq. (10) is performed, and this operator takes the following form by considering the decision maker’s weights (${\lambda _{k}}$):

Step 4: The Consistency Ratio (CR) of aggregated IVIF matrix judgments (${\tilde{R}_{I}^{k}}$ and ${\tilde{R}_{G}}$) are calculated by the following formula: In this formula, $RI$ is the random index given in Table 6, n shows the matrix elements’ number and finally, ${\textstyle\prod _{ij}^{U}}(x)$ shows the hesitation value. If CR ⩽ 0.10, IVIF judgment matrices are considered as consistent. Otherwise, the judgment matrices should be reviewed.

Step 5: Criteria weights (${w_{j}}$) are calculated by the following formula In this formula, ${\tilde{w}_{j}}$ is the entropy weight of the jth criterion. There are several formulations for the entropy weight. In this paper, the formula proposed by Wei et al. (2011) is used: The criteria weights will be used as an input while performing IVIF MABAC method in this paper.

MABAC (Multi-Attribute Border Approximation area Comparison) is one of the MCDM methods, and it was introduced by Pamučar and Ćirović (2015). The main idea of this method is defining the border approximation area for each criterion. An alternative is located at the border, upper or lower approximation areas. The upper and lower approximation areas contain the ideal and anti-ideal alternatives, respectively. Finally, the ranking of alternatives is found (Tuş and Aytaç Adalı, 2018).

It is assumed that there are m alternatives, ${A_{i}}$ $(i=1,2,\dots ,m)$, n criteria ${C_{j}}$ $(j=1,2,\dots ,n)$, K decision makers, DM_k $(k=1,2,\dots ,K)$ in the problem. IVIF MABAC method’s steps are presented in the following (Xue et al., 2016; Liu et al., 2019):

Step 1: Each decision maker is asked to assess the performance of different alternatives under various criteria by using the linguistic term presented in Table 7. They are represented by the IVIFNs.

The IVIF decision matrix of the kth decision maker (${\tilde{X}^{k}}$) is formed as: where ${\tilde{x}_{ij}^{k}}=[{\mu ^{L}}({\tilde{x}_{ij}^{k}}),{\mu ^{U}}({\tilde{x}_{ij}^{k}})],[{v^{L}}({\tilde{x}_{ij}^{k}}),{v^{U}}({\tilde{x}_{ij}^{k}})]$, ${\tilde{x}_{ij}}$ is IVIFN indicating the value of ith alternative on jth criterion.

Step 2: After obtaining the assessments of decision makers, all individual decision matrices (${\tilde{X}^{k}}$) are aggregated. The result is group IVIF decision matrix (${\tilde{X}^{G}}$), and it is formed as: where ${\tilde{x}_{ij}}$ is IVIFN indicating the aggregated performance value of ith alternative on jth criterion. The aggregation of all individual decision matrices is performed by using the IVIFWA operator given in Eq. (10). This operator takes the following form by taking into account the decision maker’s weights (${\lambda _{k}}$):

Step 3: Normalized decision matrix $\tilde{N}={[{\tilde{n}_{ij}}]_{mxn}}$ is obtained. However, the decision matrix is not normalized as Zavadskas et al. (2015) stated that IVIFNs are commensurable numbers (Zavadskas et al., 2015).

Step 4: The weighted group IVIF decision matrix ($\tilde{R}$) is calculated. ${\tilde{r}_{ij}}=[{\mu ^{L}}({\tilde{r}_{ij}}),{\mu ^{U}}({\tilde{r}_{ij}})],[{v^{L}}({\tilde{r}_{ij}}),{v^{U}}({\tilde{r}_{ij}})]$ is the weighted IVIFN indicating the elements of $\tilde{R}$. ${\tilde{r}_{ij}}$ is calculated as follows: ${w_{j}}$is jth criterion’s weight. The criteria weights are derived from IVIF AHP in this paper.

Step 5: Border approximation area vector, $\tilde{G}=[{\tilde{g}_{1}},{\tilde{g}_{2}},\dots ,{\tilde{g}_{n}}]$, is determined. The elements of the $\tilde{G}({\tilde{g}_{j}})$ indicate the border approximation area for each criterion. ${\tilde{g}_{j}}$ is represented by IVIFN as ${\tilde{g}_{j}}=[{\mu ^{L}}({\tilde{g}_{j}}),{\mu ^{U}}({\tilde{g}_{j}})],[{v^{L}}({\tilde{g}_{j}}),{v^{U}}({\tilde{g}_{j}})]$, and its value is found by using the IVIFGA operator as:

Step 6: Distance matrix of the alternatives from the border approximation area, $D={[{d_{ij}}]_{mxn}}$, is calculated. The necessary operation for finding the elements of $D({d_{ij}})$ is as follows: ${d_{E}}({\tilde{r}_{ij}},{\tilde{g}_{j}})$ is Euclidean distance between ith alternative and the border approximation area. The IVIF Euclidean distance operator in Eq. (12) is performed. The desirability of ith alternative (${A_{i}}$) is determined by analysing the distance value as follows:

${A_{i}}$ should be located at the upper approximate area (${G^{+}}$) under many criteria for being the best. A higher value ${g_{i}}\in {G^{+}}$ and a smaller value ${g_{i}}\in {G^{-}}$ show that ${A_{i}}$ is closer to the ideal and anti-ideal alternative, respectively.

Step 7. Ranking of alternatives are obtained with criteria functions values (${S_{i}}$). The alternative with the highest ${S_{i}}$ value is assumed as the best alternative.

The methodology described above under different headings is summarized as a flowchart in Fig. 1.

In this study, criteria weights are calculated with the IVIF AHP method. As it is known, the AHP method is one of the subjective methods, in other words, the criteria weights are based on the opinions of decision makers. When the decision makers or their opinions change, the criteria weights change accordingly. Therefore, in this part of the study, sensitivity analysis is carried out to determine how sensitive the IVIF MABAC method is to changes in decision makers’ weights and criteria weights. To analyse this, firstly the decision makers’ weights are changed. 5 different cases are generated and the ranking of the hybrid vehicle alternatives is obtained by considering these weights. The weights of the decision makers and the rankings obtained are given in Table 18. The first case is the weights obtained by using the entropy method in the previous section. In this case, the four decision makers’ weights are quite close to each other. The other cases assume that there is only one decision maker in the decision problem. The hybrid vehicle alternative ranking result of the first case is A₁–A₂–A₃–A₅–A₄. This ranking is the same as the ranking where the first decision maker is effective alone (Case 2). This is due to the fact that the weight of the first decision maker is slightly more than the weights of other decision makers in the weights found by entropy. However, when we look at the cases where other decision makers are effective alone, it is observed that the ranking changes. This situation shows the sensitivity of the decision makers in the alternative ranking.

For the analysis of criteria weights, different 21 cases are firstly created regarding the criteria weights. All cases including different criteria weights are presented in Table 19. The first case is the solution given in the application section and the values obtained from IVIF AHP. In cases between Case 2 and Case 6, values of 0.30, 0.25, 0.20, 0.15, and 0.10 are taken into account as criteria weights. The cases where each criterion has the highest and lowest weight are taken into account. In cases between Case 7 and Case 11, the highest criterion weight is 0.40, and equal weight (0.15) is used in other criteria. In cases between Case 12 and Case 16, the lowest criterion weight is 0.08, while other criteria are assigned equal weight (0.23). Finally, in cases between Case 17 and Case 21, the highest criterion weight is 0.9, while other criteria are assigned equal weight (0.025).

The problem given in the application section with the different criteria weights given in Table 19 is solved with the IVIF MABAC method, and rankings for hybrid vehicle alternatives are obtained. These rankings are given in Fig. 2. When Fig. 2 is examined, it is observed that there is no change in the ranking of hybrid vehicle alternatives. According to these results, we can say that the IVIF MABAC method is not sensitive in terms of criteria weights in ranking hybrid vehicle alternatives. This can be explained by the fact that the criteria weights are not very different from each other in all 16 cases. Considering all the situations, the change in the criteria weights is not too big, at most +20% and at least −12%. Therefore, the fact that the rankings do not change shows that the method is not very sensitive to small changes. When the criteria weights are close to each other, the best alternative is A₁ and the worst alternative is A₄. This situation is an advantage for decision makers in that they can consider the same ranking if they do not change the criteria weights too much. The fact that there is no change in the rankings despite a very large change in the criteria weights can be considered a negative situation. However, it is not possible to say this for the current situation. In order to analyse this situation, Case 17–Case 21 are generated, giving each criterion much more weight than the others. It has been observed that there are changes in the rankings in these cases. This is important in terms of showing that the method is sensitive to major changes.

In this part of the study, in order to see the advantage of the proposed method, the results derived by IVIF MABAC method are compared with the results obtained by IVIF WASPAS and IVIF TOPSIS methods. The application steps of Abdullah et al. (2020) and Mishra and Rani (2018) are applied for IVIF TOPSIS and IVIF WASPAS methods, respectively. The lambda value for IVIF WASPAS method is assumed as 0.5.

The results are shown in Fig. 3. The ranking obtained by the IVIF MABAC method is the same as the ranking obtained by the IVIF TOPSIS method, but slightly different from the ranking obtained by the IVIF WASPAS method. When Fig. 3 is examined, it is seen that the ${A_{1}}$ ranks first in the IVIF MABAC and IVIF TOPSIS methods, but ranks second in the ranking according to the IVIF WASPAS method. Similar interpretations can be made for other alternatives. To prove this better, the Pearson correlation coefficient between the methods is calculated. The correlation coefficient between IVIF MABAC and IVIF TOPSIS is 100%. This shows that both methods produce the same ranking of alternatives. On the other hand, the correlation coefficient value between IVIF MABAC and IVIF WASPAS methods is found to be 80%. This can be considered a relatively high value. When we look more closely at the alternative ranking of both methods, the difference is in the alternatives A₁, A₂, A₅ and A₃. For example, alternatives A₁ and A₂ rank first and second in IVIF MABAC method, while they rank second and first in the IVIF WASPAS method. A similar situation can also be applied to A₃ and A₅ alternatives. The last ranked alternative (A₄) remains unchanged in both methods. The computed crisp final scores of A₂ and A₁ are very close to each other, namely 0.873 and 0.867, respectively. These similarities in alternative rankings suggest that the IVIF MABAC method produces adequate and satisfactory results for current application. However, it should be noted that these rankings may change as the weights assigned to the criteria and decision makers change.

These three methods are also compared with respect to the time complexity as Aytaç Adalı and Tuş (2023), Alkahtani et al. (2019), Aytaç Adalı et al. (2023), and Rani et al. (2021) performed in their studies. Considering there are m alternatives and n criteria, IVIF MABAC method requires 4mn operations for the decision matrix, 4mn operations for the weighted decision matrix, 4n operations for border approximation area matrix, mn operations for Euclidean distances of each alternative, 2mn+n operations for distance matrix, and m operations for the ranking of the alternatives. In this manner, the time complexity of IVIF MABAC method is 11mn+5n+m. IVIF-WASPAS method requires 4mn operations for the decision matrix, 4mn+2m(n−1)+2m operations for relative weight according to WSM (Weighted Sum Model), 4mn+2m(n−1)+2m operations for relative weight according to WPM (Weighted Product Model), 12m operations for total relative importance and m operations for the ranking of the alternatives. So, the time complexity of IVIF-WASPAS method is 16mn+13m. IVIF-TOPSIS method requires 4mn operations for the decision matrix, 4mn operations for the weighted decision matrix, 4n+m operations for determining the positive and negative ideal solutions, and m operations for the ranking of the alternatives. The time complexity of IVIF-TOPSIS method is 8mn+8n+3m. According to this computational complexity analysis for these three methods, IVIF-WASPAS method shows the worst performance in terms of the number of operations. Although IVIF-TOPSIS method has a minimum number of operations, the operations performed to find positive and negative ideal solutions are much more complex than the operations performed to find the distance matrix in the IVIF MABAC method. In this respect, IVIF MABAC method can be considered as an alternative method to the IVIF-TOPSIS method.